Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene

Is that allowed, so you can hold a pair, and reroll the other 3 dice?

You say a 3 of a kind gets a "free roll".

Does that mean you roll all 5 dice again?

Also, is any money added to the pot after it hits, or does it start from zero? What happens when someone rolls a four of a kind with less than $100 in the pot (think multiple hits in short succession)?

Quote:GenoDRPhHello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene

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Welcome to the forum! It's always good to take a peek at the forum rules: Forum Rules.

The analysis you are asking for is straightforward and relatively easy. I'm busy and can't do it right now, but I'm sure someone will step up shortly.

Gene

The actual number is probably lower, and I'm happy to hear why.

Quote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

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It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

Quote:unJonQuote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

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It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

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... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.

Quote:DieterQuote:unJonQuote:DieterAssuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.

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It’s lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.

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... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.

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I don’t follow that comment. You know the prize pool when you roll. One person rolls at a time.

6^5 = 7,776 ways to roll 5 dice.

6 ways to roll 5OAK

150 ways to roll 4OAK

1,500 ways to roll 3OAK (includes full houses)

Pot is $X

6 * 0.85 * X + 150 * 100 + 1,500 * Y - (7,776 - 1,500 - 150 - 6) = 0

Y is recursive EV of playing the game again. Will calculate when back in front of Excel.

What am

I missing?

Quote:unJonI take it back. The game doesn’t make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldn’t build, it should drain from the 4OAKs.

What am

I missing?

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Dang.

Well... guess I need to go look for a pub. ;)

(I will not use any superpowers in furtherance of this effort. I also know that a common rule is 1 shake per day.)

Quote:unJonI take it back. The game doesn’t make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldn’t build, it should drain from the 4OAKs.

What am

I missing?

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My analysis agrees with unjon's posts. Perhaps something in the statement of the rules isn't accurate?.

Are we sure that any 4oak pays $100, and not just four 6s? Or, that the first 4 dice must be a 4oak?

The first roll is irrelevant. The second roll has to match the first roll to allow a third roll (P=1/6). The third roll has to match, else you lose. You earn a free roll (unless your fourth roll matches). (So the probability of this is 1/36 - 1/216 = 5/216, I have assumed you have the option of having your $1 returned for the break-even point.)

Fourth matching roll earns $100 (probability of this is 1 in 216, but you take off the probability of jackpot to give 5/1296) so this represents about 38.58c.

Fifth matching earns whatever (it shouldn't be more than $766, or about $900 if the bar tender get 15%, else positive for the player!)

Event | Probability | Pays | Contribution |
---|---|---|---|

3 not 4 | .023148 | $1 | $0.02 315c |

4 not 5 | .003858 | $100 | $0.38 580c |

5 jackpot | .000772 | $901.18 | $0.59 105c |

$1.00 000c |

Quote:charliepatrickThe maths sorts of works if you roll one die at a time and lose once you fail to get the recent roll to match.

The first roll is irrelevant. The second roll has to match the first roll to allow a third roll (P=1/6). The third roll has to match, else you lose. You earn a free roll (unless your fourth roll matches). (So the probability of this is 1/36 - 1/216 = 5/216, I have assumed you have the option of having your $1 returned for the break-even point.)

Fourth matching roll earns $100 (probability of this is 1 in 216, but you take off the probability of jackpot to give 5/1296) so this represents about 38.58c.

Fifth matching earns whatever (it shouldn't be more than $766, or about $900 if the bar tender get 15%, else positive for the player!)

Event Probability Pays Contribution 3 not 4 .023148 $1 $0.02 315c4 not 5 .003858 $100 $0.38 580c5 jackpot .000772 $901.18 $0.59 105c $1.00 000c

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Excellent math sleuthing. You’ll get a more accurate result if instead of using $1 for 3OAK you just juice the probabilities of the 4OAK and 5OAK by the 102.3697%.

Basically the sum from n=1 to infinity of (5/216)^n.

ETA: oh I see, $1 for break even on 3OAK.

As others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.Quote:BillHasRetiredI don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

Quote:unJonI take it back. The game doesn’t make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldn’t build, it should drain from the 4OAKs.

What am

I missing?

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You are missing the address of the pub! And yes, that is Axel at the end of the bar rolling the dice….

Quote:charliepatrickAs others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.Quote:BillHasRetiredI don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

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1. I think you get to play once a day.

2. I think you have to buy a drink to be allowed to play.

The game may be positive, but I don't think it's profitable to the player.

That said, if you're down at the bar anyway...

Quote:charliepatrickAs others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.Quote:BillHasRetiredI don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

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1. I think you get to play once a day.

2. I think you have to buy a drink to be allowed to play.

The game may be positive, but I don't think it's profitable to the player.

That said, if you're down at the bar anyway...

The OP said there is no rake other than the tip for the top payout. So basically a tip for a guest getting a jackpot of sorts

I think we are all too much into figuring out the negative EV.

The games positive EV for the house is simply that they drum up business for their pub, make an occasional jackpot winner happy (spreading the word) and they even get to share in that persons jackpot.

It also doesn't sound like an official game so maybe a negative expectation game would be illegal? Usually that's why a house doesn't take a rake

Also since it's players money going into the pot even though it's positive EV you would have to wait for it to get to a decent size. The object isn't to just win back your own money

Quote:avianrandyHave you been back to the pub lately? What are the exact rules for this game?

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Haven't been back since before COVID, A hospitalization, then COVID, then a move to another part of town. It was withing walking distance, and unless I know I'm going to just get one drink and nurse it all night I don't drink and get behind the wheel, so it's not worth the risk of a drive. If I even find myself back there, I'll be sure to inquire of the rules and update.

Quote:darkozBeing a bar pub game it may very well be +EV.

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Am I missing something obvious?

There are 7776 results from rolling 5 dice.

150 of them are four of a kind.

Even if any roll besides a four of a kind paid nothing, the EV is 150 x 100 / 7776 - 1 = 0.929.

the triple DOES NOT pay $1 its WORTH $1. this is the same as a lotto giving a 'free ticket' instead of paying the $1. Since the $1 DOES NOT come out of the pot, the Triples chance is added back into the game AS POSTED. The Chance of ANY 5oK is still 6^5/6 = 6^4 = 1296. My 'corrected' pay is $796. After the15% tip, $676.6

I will offer another view...

4/5 = 100/216 (6^5/6)/6

the remaining fraction pays the 5/5 = $696... after the tip $591.6

There was a bar about 10mi. away (but up the street from where i worked) that had this exact game and pay. Its easy to think $1296 is B/E but the pays of 4oK lowers it. A rule of thumb is $700+ is AP.

Quote:NotSoFun21sorry to revive this but something bothers me...

the triple DOES NOT pay $1 its WORTH $1. this is the same as a lotto giving a 'free ticket' instead of paying the $1. Since the $1 DOES NOT come out of the pot, the Triples chance is added back into the game AS POSTED. The Chance of ANY 5oK is still 6^5/6 = 6^4 = 1296. My 'corrected' pay is $796. After the15% tip, $676.6

I will offer another view...

4/5 = 100/216 (6^5/6)/6

the remaining fraction pays the 5/5 = $696... after the tip $591.6

There was a bar about 10mi. away (but up the street from where i worked) that had this exact game and pay. Its easy to think $1296 is B/E but the pays of 4oK lowers it. A rule of thumb is $700+ is AP.

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Sorry I’m not following your middle paragraph. What’s wrong with the logic that any amount above $100 is AP since $100 for 4OAK is +EV on its own?

i made a mistake calculating this, and have clarified. the payment is 100/259.2 which is NOT AP, and further, it reduces the jackpot when hit.

The correct answer is based upon 1296 rolls of the dice.

The chance of 4 of 5 is 6*6*6*6*6/(6*5) = 1 in 259.2

There will be 125/648 fewer $'s in the pot because of the 'free rolls'.

So the JP at 100% payout is 1-(125/648+100/259.2) = 1 - 0.5787 = 0.4213 times 1296 = $546

You get 85% or $464

If you want to win 100% after the tip, the JP must be 546/0.85 = $642 or better.

sorry for the confusion and error

NSF21

Quote:NotSoFun21the odds of 4/5 is 6*6*6*6*6 divided by the 6 ranks which is then divided by the 5 ways that the 4oK can occur = 7776/30

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Er, if you are counting every possible 4OAK, isn't it 6*6*6*6*6 divided by the 6 ranks and then divided by the 25 ways it can occur?

e.g. for four 6s:

1 6 6 6 6

2 6 6 6 6

3 6 6 6 6

4 6 6 6 6

5 6 6 6 6

6 1 6 6 6

6 2 6 6 6

6 3 6 6 6

6 4 6 6 6

6 5 6 6 6

6 6 1 6 6

6 6 2 6 6

6 6 3 6 6

6 6 4 6 6

6 6 5 6 6

6 6 6 1 6

6 6 6 2 6

6 6 6 3 6

6 6 6 4 6

6 6 6 5 6

6 6 6 6 1

6 6 6 6 2

6 6 6 6 3

6 6 6 6 4

6 6 6 6 5

Quote:NotSoFun21thanks for that, i see the results you speak of. yes. So the odds are 6^5/150 not 30. Thus 1 in 51.84 (1/5 of my answer).

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Right. Making it +EV from the get go as long as there is enough in the pot to pay out the 4OAK.